Standing waves for quasilinear Schrödinger equations involving double exponential growth

Yony Raúl Santaria Leuyacc

doi:10.3934/math.2023086

Standing waves for quasilinear Schrödinger equations involving double exponential growth

Yony Raúl Santaria Leuyacc

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B₁ denotes the unit ball centered at the origin in R² and g behaves like exp(e^s4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.

Original language	English
Pages (from-to)	1682-1695
Number of pages	14
Journal	AIMS Mathematics
Volume	8
Issue number	1
DOIs	https://doi.org/10.3934/math.2023086
State	Published - 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Trudinger-Moser inequality
double exponential growth
dual approach
mountain pass theorem
quasilinear Schrödinger equation

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10.3934/math.2023086

Cite this

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abstract = "We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schr{\"o}dinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.",

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Standing waves for quasilinear Schrödinger equations involving double exponential growth

Abstract

Bibliographical note

Keywords

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